Analysis
Below is a figure reflecting how the speed at which retweeting occurs evolves as the message spreads across users.
It can be seen above that there are three exceptionally viral tweets which take off at very high speeds - about 80 retweets per second to up to 160 retweets per second. All the three tweets are from user(s) on the higher end of the follower count (light blue). In comparison, there is a dark blue line (representing a tweet from a user with lower number of followers) which spreads at a slower speed but also reaches a lot of users ~20,000 in a span of 90 minutes.
Elite versus Ordinary Users
The underlying mechanism here seems to be the following. Imagine a network where there is one “elite” (central) node, connected to a lot of other “normal” nodes that are all identical. Each normal node has a certain probability with which it decides to retweet a tweet. When the elite tweets, the retweets would spread really fast at first, but then slow down and fall to zero as the probabilities of normal users not retweeting compounds. A few of Katy Perry’s tweets reflect this behavior:
In a real network there are many elites, so if a tweet created by a normal user is retweeted by an elite, the aforementioned dynamic would occur. This would make an otherwise falling speed profile to rise, and the rise would depend on how “elite” the node was that retweeted the original tweet. Below is such a case. The user @danibucaro had 488 followers when she created the tweet4 The top posts in the thread read: “@danibucaro I’m so proud to know you. You’ve made me proud 😍😍”,“finally getting the recognition u deserve”, etc. which went viral and has got retweeted 90K times until today.
In that way, it appears that the measures developed above can be handy to identify what might be called “organically” created content which went viral.
Clinton versus Trump
It is also possible that a group of users (or bots) organize in order to retweet a tweet rapidly. This would not be distinguishable from an elite-driven speed boost in the current analysis. For instance, it can be seen below that there are some unique patterns in Trump’s retweets that do not show in Clinton’s. At this point it is unclear what is causing the huge boosts in retweeting speed for Trump’s tweets once it is retweeted by around 1000 - 2500 users.
It can also be seen that Clinton’s tweets start with speeds that are about 4-5 times higher than Trump’s tweets, and she also has many more viral tweets in general (see plot on the right). However, this comparison cannot be made with confidence because the the dataset consists only of a subset of all the tweets made by the two candidates (where they explicitly mention either Trump or Clinton), as noted in the beginning.